Recursive generation of one-loop amplitudes in the Standard Model

Abstract

Abstract:We introduce the computer code Recola for the recursive generation of tree-level and oneloop amplitudes in the Standard Model. Tree-level amplitudes are constructed using off-shell currents instead of Feynman diagrams as basic building blocks. One-loop amplitudes are represented as linear combinations of tensor integrals whose coefficients are calculated similarly to the tree-level amplitudes by recursive construction of loop off-shell currents. We introduce a novel algorithm for the treatment of colour, assigning a colour structure to each off-shell current which enables us to recursively construct the colour structure of the amplitude efficiently. Recola is interfaced with a tensor-integral library and provides complete one-loop Standard Model amplitudes including rational terms and counterterms. As a first application we consider Z + 2 jets production at the LHC and calculate with Recola the next-to-leading-order electroweak corrections to the dominant partonic channels.

Electroweak corrections to lepton pair production in association with two hard jets at the LHC

“…For EW corrections, the situation is more involved and a complete automatisation has not been achieved yet, while different groups are working in this direction [12,13]. Recently we have developed the code Recola [14,15] which performs efficient calculations of tree-level and one-loop amplitudes in the full SM. Recola uses an alternative approach to Feynman diagrams, based on recursion relations for offshell currents.…”

“…In ref. [14] we performed a first study of EW corrections to the process pp → Z+2 jets with an on-shell Z boson. Restricting our attention to the dominant partonic processes involving external gluons, q g → q g Z,q g →q g Z, g g → qq Z, qq → g g Z, we found small EW effects on the total cross section at the level of −1%, while transversemomentum distributions received enhanced corrections at high p T (up to −25% for p T ≃ 1 TeV), owing to EW Sudakov logarithms.…”

“…For the calculation of the differential cross section at LO and NLO we follow closely the implementation of Z+2 jet production in ref. [14]. Potentially resonant Z-boson propagators are described attributing a complex mass…”

“…The calculation has been performed with Recola [14,15], which provides all relevant amplitudes for tree level, one loop and real radiation, as well as the colour-correlated squared matrix elements required for the subtraction terms. For the evaluation of the loop integrals Recola uses the tensor-integral library Collier [17,18].…”

Soft evolution of multi-jet final states

“…Next-to-leading order (NLO) corrections have also reached a high level of automation [7][8][9][10][11][12][13][14][15][16][17], and fully differential multi-jet cross…”